## [0] flags are bits
$${\frac{{{f_{0}\left(x\right)}}^{{2}} - {f_{0}\left(x\right)}}{{x}^{{\frac{T}{{2}}}} - {1}}}$$
## [1] flags_extra are bits
$${\frac{{{f_{0}\left(xg^{3}\right)}}^{{2}} - {f_{0}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [2] instruction format
$${\frac{{f_{4}\left(xg^{3}\right)} - \left(\left(\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{1}\left(xg^{11}\right)} \cdot 2^{192}+{f_{1}\left(xg^{10}\right)} \cdot 2^{176}+{f_{1}\left(xg^{9}\right)} \cdot 2^{160}+{f_{1}\left(xg^{8}\right)} \cdot 2^{144}+{f_{1}\left(xg^{7}\right)} \cdot 2^{128}+{f_{1}\left(xg^{6}\right)} \cdot 2^{112}+{f_{1}\left(xg^{5}\right)} \cdot 2^{96}+{f_{1}\left(xg^{4}\right)} \cdot 2^{80}+{f_{1}\left(xg^{3}\right)} \cdot 2^{64}+{f_{1}\left(xg^{2}\right)} \cdot 2^{48}+{f_{1}\left(xg\right)} \cdot 2^{32}+{f_{1}\left(x\right)} \cdot 2^{16}\right) + {f_{0}\left(xg^{4}\right)} \cdot \left({f_{1}\left(xg^{15}\right)} \cdot 2^{240}+{f_{1}\left(xg^{14}\right)} \cdot 2^{224}+{f_{1}\left(xg^{13}\right)} \cdot 2^{208}+{f_{1}\left(xg^{12}\right)} \cdot 2^{192}+{f_{1}\left(xg^{10}\right)} \cdot 2^{176}+{f_{1}\left(xg^{9}\right)} \cdot 2^{160}+{f_{1}\left(xg^{8}\right)} \cdot 2^{144}+{f_{1}\left(xg^{7}\right)} \cdot 2^{128}+{f_{1}\left(xg^{6}\right)} \cdot 2^{112}+{f_{1}\left(xg^{5}\right)} \cdot 2^{96}+{f_{1}\left(xg^{4}\right)} \cdot 2^{80}+{f_{1}\left(xg^{3}\right)} \cdot 2^{64}+{f_{1}\left(xg^{2}\right)} \cdot 2^{48}+{f_{1}\left(xg\right)} \cdot 2^{32}+{f_{1}\left(x\right)} \cdot 2^{16}\right)\right) \cdot 2^{251}+{f_{0}\left(xg^{15}\right)} \cdot 2^{11}+{f_{0}\left(xg^{11}\right)} \cdot 2^{10}+{f_{0}\left(xg^{7}\right)} \cdot 2^{9}+{f_{0}\left(xg^{3}\right)} \cdot 2^{8}+{f_{0}\left(xg^{12}\right)} \cdot 2^{7}+{f_{0}\left(xg^{10}\right)} \cdot 2^{6}+{f_{0}\left(xg^{8}\right)} \cdot 2^{5}+{f_{0}\left(xg^{6}\right)} \cdot 2^{4}+{f_{0}\left(xg^{4}\right)} \cdot 2^{3}+{f_{0}\left(xg^{2}\right)} \cdot 2^{2}+{f_{0}\left(x\right)} \cdot 2^{1}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [3] inst_final
$${\frac{{f_{4}\left(xg^{3}\right)} - {\mathrm{4001c00040004000c0014000400040014000400040004000000}_{16}}}{{x}^{{\frac{T}{T}}} - {g}^{T - {16}}}}$$
## [4] op1_base_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{4}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(x\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [5] op1_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{5}\right)} - \left({f_{4}\left(xg^{4}\right)} + {f_{1}\left(xg\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [6] op2_base_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{6}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{3}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [7] op2_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{7}\right)} - \left({f_{4}\left(xg^{6}\right)} + {f_{1}\left(xg^{4}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [8] dst_base_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{8}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{6}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [9] dst_addr
$${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{9}\right)} - \left({f_{4}\left(xg^{8}\right)} + {f_{1}\left(xg^{7}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [10] v1_op1_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{4}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(x\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [11] v1_op2_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{5}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [12] v1_dst_base_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{6}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [13] v1_dst_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{7}\right)} - \left({f_{4}\left(xg^{6}\right)} + {f_{1}\left(xg^{3}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [14] v1_sum
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{4}\right)} + {f_{4}\left(xg^{5}\right)} - \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{4}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [15] v2_op1_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{8}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [16] v2_op2_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{9}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg^{6}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [17] v2_dst_base_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{10}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{7}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [18] v2_dst_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{11}\right)} - \left({f_{4}\left(xg^{10}\right)} + {f_{1}\left(xg^{8}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [19] v2_sum
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{8}\right)} + {f_{4}\left(xg^{9}\right)} - \left({f_{4}\left(xg^{11}\right)} + {f_{1}\left(xg^{9}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [20] v3_op1_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{12}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{10}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [21] v3_op2_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{13}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg^{12}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [22] v3_dst_base_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{14}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{13}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [23] v3_dst_addr
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{15}\right)} - \left({f_{4}\left(xg^{14}\right)} + {f_{1}\left(xg^{14}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [24] v3_sum
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{12}\right)} + {f_{4}\left(xg^{13}\right)} - \left({f_{4}\left(xg^{15}\right)} + {f_{1}\left(xg^{15}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [25] op3_base_addr
$${\frac{\left({f_{0}\left(xg^{6}\right)} + {f_{0}\left(xg^{8}\right)} + {f_{0}\left(xg^{10}\right)}\right) \cdot \left({f_{3}\left(xg^{10}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{9}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [26] op3_addr
$${\frac{\left({f_{0}\left(xg^{6}\right)} + {f_{0}\left(xg^{8}\right)} + {f_{0}\left(xg^{10}\right)}\right) \cdot \left({f_{3}\left(xg^{11}\right)} - \left({f_{4}\left(xg^{10}\right)} + {f_{1}\left(xg^{10}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [27] cnt_init
$${\frac{{f_{3}\left(x\right)} - \mathrm{cnt\_init}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [28] cnt -> cnt
$${\frac{{f_{3}\left(x\right)} - {f_{4}\left(x\right)}}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [29] cnt update
$${\frac{\left({f_{3}\left(xg^{16}\right)} - \left({f_{3}\left(x\right)} + \left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{1}\left(xg^{11}\right)} - {32768}\right) + {f_{0}\left(xg^{4}\right)} \cdot \left({f_{0}\left(xg^{15}\right)} \cdot 2^{4}+{f_{0}\left(xg^{11}\right)} \cdot 2^{3}+{f_{0}\left(xg^{7}\right)} \cdot 2^{2}+{f_{0}\left(xg^{3}\right)} \cdot 2^{1}\right)\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [30] rbp_addr
$${\frac{{f_{3}\left(xg\right)} - \left({f_{3}\left(x\right)} + {1}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [31] pc_addr
$${\frac{{f_{3}\left(xg^{2}\right)} - \left({f_{3}\left(x\right)} + {2}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [32] mul
$${\frac{{f_{0}\left(xg\right)} - \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right) \cdot \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [33] res
$${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot {f_{0}\left(xg^{5}\right)} - \left({f_{0}\left(x\right)} \cdot {f_{0}\left(xg\right)} + {f_{0}\left(xg^{2}\right)} \cdot \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768} + \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right) + {f_{0}\left(xg^{6}\right)} \cdot {f_{4}\left(xg^{11}\right)} - {f_{0}\left(xg^{8}\right)} \cdot {f_{4}\left(xg^{11}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [34] dst = res if not jnz
$${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right) + {f_{0}\left(xg^{4}\right)}\right)\right) \cdot \left({f_{4}\left(xg^{9}\right)} + {f_{1}\left(xg^{8}\right)} - {32768} - {f_{0}\left(xg^{5}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [35] t0
$${\frac{{f_{0}\left(xg^{9}\right)} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right) \cdot \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [36] t1
$${\frac{{f_{0}\left(xg^{13}\right)} - {f_{0}\left(xg^{9}\right)} \cdot {f_{0}\left(xg^{5}\right)}}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [37] jnz fallback
$${\frac{\left({f_{0}\left(xg^{13}\right)} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{4}\left(xg^{9}\right)} + {f_{1}\left(xg^{8}\right)} - {32768}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [38] jnz jump
$${\frac{{f_{0}\left(xg^{9}\right)} \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [39] next_pc
$${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{3}\left(xg^{3}\right)} + {1}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [40] next_rbp
$${\frac{\left({f_{3}\left(xg^{9}\right)} - {f_{3}\left(xg^{17}\right)}\right) \cdot \left({f_{4}\left(xg^{17}\right)} - {f_{4}\left(xg\right)}\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [41] next_rbp vadd3
$${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{17}\right)} - {f_{4}\left(xg\right)}\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [42] lo_lo16
$${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{12}\right)} - {f_{1}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [43] lo_hi16
$${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{13}\right)} - {f_{1}\left(xg^{13}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [44] hi_lo16
$${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{14}\right)} - {f_{1}\left(xg^{14}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [45] hi_hi16
$${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{15}\right)} - {f_{1}\left(xg^{15}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [46] op3_64
$${\frac{{f_{0}\left(xg^{10}\right)} \cdot \left({f_{4}\left(xg^{11}\right)} - \left({f_{1}\left(xg^{15}\right)} \cdot 2^{64}+{f_{1}\left(xg^{14}\right)} \cdot 2^{48}+{f_{1}\left(xg^{13}\right)} \cdot 2^{32}+{f_{1}\left(xg^{12}\right)} \cdot 2^{16}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [47] mem_perm_init
$${\frac{{z_\mathrm{mem}} - \left({f_{3}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{4}\left(x\right)}\right) - {f_{23}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{5}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{6}\left(x\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [48] mem_perm_final
$${\frac{{f_{27}\left(xg^{(1/1)T + -2}\right)} - \mathrm{mem\_pub\_final}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [49] mem_addr_min
$${\frac{{f_{5}\left(x\right)} - \mathrm{mem\_addr.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [50] mem_addr_max
$${\frac{{f_{19}\left(xg^{(1/1)T + -2}\right)} - \mathrm{mem\_addr.max}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [51] rc16_perm_init
$${\frac{{z_\mathrm{rc16}} - {f_{1}\left(x\right)} - {f_{24}\left(x\right)} \cdot \left({z_\mathrm{rc16}} - {f_{2}\left(x\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [52] rc16_perm_step
$${\frac{\left({f_{24}\left(x\right)} \cdot \left({z_\mathrm{rc16}} - {f_{1}\left(xg\right)}\right) - {f_{24}\left(xg\right)} \cdot \left({z_\mathrm{rc16}} - {f_{2}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [53] rc16_perm_final
$${\frac{{f_{24}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$
## [54] rc16_min
$${\frac{{f_{2}\left(x\right)} - \mathrm{rc16.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [55] rc16_max
$${\frac{{f_{2}\left(x\right)} - \mathrm{rc16.max}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$
## [56] s_rc16 is diff-continuous
$${\frac{\left({f_{2}\left(xg\right)} - {f_{2}\left(x\right)}\right) \cdot \left({f_{2}\left(xg\right)} - {f_{2}\left(x\right)} - {f_{21}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [57] s_rc16_diff is 2-continuous
$${\frac{\left({f_{22}\left(xg\right)} - {f_{22}\left(x\right)}\right) \cdot \left({f_{22}\left(xg\right)} - {2} \cdot {f_{22}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [58] rc16_diff_perm_init
$${\frac{{z_{\delta\mathrm{rc16}}} - {f_{21}\left(x\right)} - {f_{28}\left(x\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{22}\left(x\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [59] rc16_diff_perm_step
$${\frac{\left({f_{28}\left(x\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{21}\left(xg\right)}\right) - {f_{28}\left(xg\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{22}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [60] rc16_diff_perm_final
$${\frac{{f_{28}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$
## [61] rc16_diff_min
$${\frac{{f_{22}\left(x\right)} - \mathrm{rc16\_diff.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [62] rc16_diff_max
$${\frac{{f_{22}\left(x\right)} - \mathrm{rc16\_diff.max}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$
## [63] s_mem_addr is continuous at 0
$${\frac{\left({\left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)}\right)}^{{2}} - \left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [64] (s_mem_addr, s_mem_val) is a function at 0
$${\frac{\left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)} - {1}\right) \cdot \left({f_{6}\left(xg\right)} - {f_{6}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [65] mem_perm_step at 0
$${\frac{\left({f_{23}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{3}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{4}\left(xg\right)}\right)\right) - {f_{23}\left(xg\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{5}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{6}\left(xg\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [66] s_mem_addr is continuous at (1/1)T + -1
$${\frac{{\left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [67] (s_mem_addr, s_mem_val) is a function at (1/1)T + -1
$${\frac{\left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{12}\right)} - {f_{6}\left(xg^{(1/1)T + -1}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [68] mem_perm_step at (1/1)T + -1
$${\frac{{f_{23}\left(xg^{(1/1)T + -1}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{12}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [69] s_mem_addr is continuous at (1/1)T + 0
$${\frac{{\left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [70] (s_mem_addr, s_mem_val) is a function at (1/1)T + 0
$${\frac{\left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{28}\right)} - {f_{13}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [71] mem_perm_step at (1/1)T + 0
$${\frac{{f_{25}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{12}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{12}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{20}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{28}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [72] s_mem_addr is continuous at (1/1)T + 1
$${\frac{{\left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [73] (s_mem_addr, s_mem_val) is a function at (1/1)T + 1
$${\frac{\left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{44}\right)} - {f_{13}\left(xg^{28}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [74] mem_perm_step at (1/1)T + 1
$${\frac{{f_{25}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{36}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{44}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [75] s_mem_addr is continuous at (1/1)T + 2
$${\frac{{\left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [76] (s_mem_addr, s_mem_val) is a function at (1/1)T + 2
$${\frac{\left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{60}\right)} - {f_{13}\left(xg^{44}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [77] mem_perm_step at (1/1)T + 2
$${\frac{{f_{25}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{52}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{60}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [78] s_mem_addr is continuous at (1/1)T + 3
$${\frac{{\left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [79] (s_mem_addr, s_mem_val) is a function at (1/1)T + 3
$${\frac{\left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{76}\right)} - {f_{13}\left(xg^{60}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [80] mem_perm_step at (1/1)T + 3
$${\frac{{f_{25}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{12}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{12}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{68}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{76}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [81] s_mem_addr is continuous at (1/1)T + 4
$${\frac{{\left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [82] (s_mem_addr, s_mem_val) is a function at (1/1)T + 4
$${\frac{\left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{92}\right)} - {f_{13}\left(xg^{76}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [83] mem_perm_step at (1/1)T + 4
$${\frac{{f_{25}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{84}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{92}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [84] s_mem_addr is continuous at (1/1)T + 5
$${\frac{\left({\left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [85] (s_mem_addr, s_mem_val) is a function at (1/1)T + 5
$${\frac{\left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{140}\right)} - {f_{13}\left(xg^{92}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [86] mem_perm_step at (1/1)T + 5
$${\frac{\left({f_{25}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{244}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{236}\right)}\right)\right) - {f_{25}\left(xg^{132}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{132}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{140}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [87] s_mem_addr is continuous at (67/64)T + -1
$${\frac{{\left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [88] (s_mem_addr, s_mem_val) is a function at (67/64)T + -1
$${\frac{\left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{12}\right)} - {f_{13}\left(xg^{(1/1)T + -36}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [89] mem_perm_step at (67/64)T + -1
$${\frac{{f_{25}\left(xg^{(1/1)T + -44}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{12}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [90] s_mem_addr is continuous at (67/64)T + 0
$${\frac{{\left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [91] (s_mem_addr, s_mem_val) is a function at (67/64)T + 0
$${\frac{\left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{28}\right)} - {f_{16}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [92] mem_perm_step at (67/64)T + 0
$${\frac{{f_{26}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{15}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{15}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{20}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{28}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [93] s_mem_addr is continuous at (67/64)T + 1
$${\frac{{\left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [94] (s_mem_addr, s_mem_val) is a function at (67/64)T + 1
$${\frac{\left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{44}\right)} - {f_{16}\left(xg^{28}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [95] mem_perm_step at (67/64)T + 1
$${\frac{{f_{26}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{36}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{44}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [96] s_mem_addr is continuous at (67/64)T + 2
$${\frac{{\left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [97] (s_mem_addr, s_mem_val) is a function at (67/64)T + 2
$${\frac{\left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{60}\right)} - {f_{16}\left(xg^{44}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [98] mem_perm_step at (67/64)T + 2
$${\frac{{f_{26}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{52}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{60}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [99] s_mem_addr is continuous at (67/64)T + 3
$${\frac{{\left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [100] (s_mem_addr, s_mem_val) is a function at (67/64)T + 3
$${\frac{\left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{76}\right)} - {f_{16}\left(xg^{60}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [101] mem_perm_step at (67/64)T + 3
$${\frac{{f_{26}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{15}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{15}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{68}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{76}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [102] s_mem_addr is continuous at (67/64)T + 4
$${\frac{{\left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [103] (s_mem_addr, s_mem_val) is a function at (67/64)T + 4
$${\frac{\left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{92}\right)} - {f_{16}\left(xg^{76}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [104] mem_perm_step at (67/64)T + 4
$${\frac{{f_{26}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{84}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{92}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [105] s_mem_addr is continuous at (67/64)T + 5
$${\frac{\left({\left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [106] (s_mem_addr, s_mem_val) is a function at (67/64)T + 5
$${\frac{\left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{140}\right)} - {f_{16}\left(xg^{92}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [107] mem_perm_step at (67/64)T + 5
$${\frac{\left({f_{26}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{244}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{236}\right)}\right)\right) - {f_{26}\left(xg^{132}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{132}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{140}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [108] s_mem_addr is continuous at (35/32)T + -1
$${\frac{{\left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [109] (s_mem_addr, s_mem_val) is a function at (35/32)T + -1
$${\frac{\left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{15}\right)} - {f_{16}\left(xg^{(1/1)T + -36}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [110] mem_perm_step at (35/32)T + -1
$${\frac{{f_{26}\left(xg^{(1/1)T + -44}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{3}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{7}\right)}\right)\right) - {f_{27}\left(xg^{3}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{11}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{15}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [111] s_mem_addr is continuous at (35/32)T + 0
$${\frac{{\left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [112] (s_mem_addr, s_mem_val) is a function at (35/32)T + 0
$${\frac{\left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{31}\right)} - {f_{20}\left(xg^{15}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [113] mem_perm_step at (35/32)T + 0
$${\frac{{f_{27}\left(xg^{3}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{19}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{23}\right)}\right)\right) - {f_{27}\left(xg^{7}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{27}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{31}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [114] s_mem_addr is continuous at (35/32)T + 1
$${\frac{{\left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [115] (s_mem_addr, s_mem_val) is a function at (35/32)T + 1
$${\frac{\left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{47}\right)} - {f_{20}\left(xg^{31}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [116] mem_perm_step at (35/32)T + 1
$${\frac{{f_{27}\left(xg^{7}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{35}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{39}\right)}\right)\right) - {f_{27}\left(xg^{11}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{43}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{47}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [117] s_mem_addr is continuous at (35/32)T + 2
$${\frac{{\left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)}\right)}^{{2}} - \left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [118] (s_mem_addr, s_mem_val) is a function at (35/32)T + 2
$${\frac{\left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)} - {1}\right) \cdot \left({f_{20}\left(x\right)} - {f_{20}\left(xg^{47}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [119] mem_perm_step at (35/32)T + 2
$${\frac{{f_{27}\left(xg^{11}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(x\right)}\right)\right) - {f_{27}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(x\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [120] s_mem_addr is continuous at (35/32)T +
$${\frac{\left({\left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)}\right)}^{{2}} - \left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)}\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [121] (s_mem_addr, s_mem_val) is a function at (35/32)T +
$${\frac{\left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)} - {1}\right) \cdot \left({f_{20}\left(xg\right)} - {f_{20}\left(x\right)}\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [122] mem_perm_step at (35/32)T +
$${\frac{\left({f_{27}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(xg\right)}\right)\right) - {f_{27}\left(xg\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg\right)}\right)\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [123] s_mem_addr is continuous at (35/32)T +
$${\frac{\left({\left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)}\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [124] (s_mem_addr, s_mem_val) is a function at (35/32)T +
$${\frac{\left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{4}\right)} - {f_{20}\left(xg^{2}\right)}\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [125] mem_perm_step at (35/32)T +
$${\frac{\left({f_{27}\left(xg^{2}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(xg^{4}\right)}\right)\right) - {f_{27}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{4}\right)}\right)\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [126] s_mem_addr is continuous at (35/32)T + 98
$${\frac{\left({\left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [127] (s_mem_addr, s_mem_val) is a function at (35/32)T + 98
$${\frac{\left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{143}\right)} - {f_{20}\left(xg^{126}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [128] mem_perm_step at (35/32)T + 98
$${\frac{\left({f_{27}\left(xg^{126}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{131}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{135}\right)}\right)\right) - {f_{27}\left(xg^{131}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{139}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{143}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [129] load_const first
$${\frac{{f_{7}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [130] load_const can decrease by bit
$${\frac{\left({\left({f_{7}\left(x\right)} - {f_{7}\left(xg\right)}\right)}^{{2}} - \left({f_{7}\left(x\right)} - {f_{7}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [131] load_const last
$${\frac{{f_{7}\left(xg^{127}\right)} - {1}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [132] load_const addresses strictly increasing
$${\frac{{f_{5}\left(xg^{383}\right)} - {f_{5}\left(x\right)} - {383}}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [133] r1 init
$${\frac{{f_{7}\left(x\right)} \cdot \left({f_{8}\left(x\right)} - {f_{6}\left(x\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [134] r2 init
$${\frac{{f_{7}\left(x\right)} \cdot \left({f_{9}\left(x\right)} - {f_{6}\left(xg^{128}\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [135] r3 init
$${\frac{{f_{7}\left(x\right)} \cdot \left({f_{10}\left(x\right)} - {f_{6}\left(xg^{256}\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [136] r1 is periodic
$${\frac{\left({f_{8}\left(xg^{128}\right)} - {f_{8}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [137] r2 is periodic
$${\frac{\left({f_{9}\left(xg^{128}\right)} - {f_{9}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [138] r3 is periodic
$${\frac{\left({f_{10}\left(xg^{128}\right)} - {f_{10}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [139] hash1-hash_start
$${\frac{{f_{11}\left(xg^{116}\right)} - \left(\mathrm{hash\_start} + 0 \cdot {6} \cdot {\frac{T}{{128}}}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [140] hash1-in2_addr = in1_addr + 1
$${\frac{{f_{12}\left(xg^{116}\right)} - {f_{11}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [141] hash1-in3_addr = in2_addr + 1
$${\frac{{f_{13}\left(xg^{116}\right)} - {f_{12}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [142] hash1-out1_addr = in3_addr + 1
$${\frac{{f_{11}\left(xg^{124}\right)} - {f_{13}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [143] hash1-out2_addr = out1_addr + 1
$${\frac{{f_{12}\left(xg^{124}\right)} - {f_{11}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [144] hash1-out3_addr = out2_addr + 1
$${\frac{{f_{13}\left(xg^{124}\right)} - {f_{12}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [145] hash1-next_in1_addr = out3_addr + 1
$${\frac{\left({f_{11}\left(xg^{244}\right)} - {f_{13}\left(xg^{124}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [146] hash1-pre_round_1
$${\frac{{f_{11}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {2} + {f_{12}\left(xg^{108}\right)} \cdot {1} + {f_{13}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [147] hash1-pre_round_2
$${\frac{{f_{12}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {1} + {f_{12}\left(xg^{108}\right)} \cdot {2} + {f_{13}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [148] hash1-pre_round_3
$${\frac{{f_{13}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {1} + {f_{12}\left(xg^{108}\right)} \cdot {1} + {f_{13}\left(xg^{108}\right)} \cdot {2}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [149] hash1-hash_full_1_sq
$${\frac{\left({f_{25}\left(x\right)} - {\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [150] hash1-hash_full_2_sq
$${\frac{\left({f_{11}\left(xg^{4}\right)} - {\left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [151] hash1-hash_full_3_sq
$${\frac{\left({f_{12}\left(xg^{4}\right)} - {\left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [152] hash1-hash_full_next1
$${\frac{\left({f_{11}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [153] hash1-hash_full_next2
$${\frac{\left({f_{12}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [154] hash1-hash_full_next3
$${\frac{\left({f_{13}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {2}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [155] hash1-hash_part_1_sq
$${\frac{\left({f_{25}\left(x\right)} - {\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [156] hash1-hash_part_next1-continuation
$${\frac{\left({f_{11}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [157] hash1-hash_part_next1-jump
$${\frac{\left({f_{11}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [158] hash1-hash_part_next2-continuation
$${\frac{\left({f_{12}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [159] hash1-hash_part_next2-jump
$${\frac{\left({f_{12}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [160] hash1-hash_part_next3-continuation
$${\frac{\left({f_{13}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [161] hash1-hash_part_next3-jump
$${\frac{\left({f_{13}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [162] hash1-hash_part_start1
$${\frac{{f_{11}\left(xg^{64}\right)} - {f_{11}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [163] hash1-hash_part_start2
$${\frac{{f_{12}\left(xg^{64}\right)} - {f_{12}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [164] hash1-hash_part_start3
$${\frac{{f_{13}\left(xg^{64}\right)} - {f_{13}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [165] hash1-hash_part_end1
$${\frac{{f_{11}\left(xg^{111}\right)} - {f_{11}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [166] hash1-hash_part_end2
$${\frac{{f_{12}\left(xg^{111}\right)} - {f_{12}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [167] hash1-hash_part_end3
$${\frac{{f_{13}\left(xg^{111}\right)} - {f_{13}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [168] hash2-hash_start
$${\frac{{f_{14}\left(xg^{116}\right)} - \left(\mathrm{hash\_start} + {1} \cdot {6} \cdot {\frac{T}{{128}}}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [169] hash2-in2_addr = in1_addr + 1
$${\frac{{f_{15}\left(xg^{116}\right)} - {f_{14}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [170] hash2-in3_addr = in2_addr + 1
$${\frac{{f_{16}\left(xg^{116}\right)} - {f_{15}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [171] hash2-out1_addr = in3_addr + 1
$${\frac{{f_{14}\left(xg^{124}\right)} - {f_{16}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [172] hash2-out2_addr = out1_addr + 1
$${\frac{{f_{15}\left(xg^{124}\right)} - {f_{14}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [173] hash2-out3_addr = out2_addr + 1
$${\frac{{f_{16}\left(xg^{124}\right)} - {f_{15}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [174] hash2-next_in1_addr = out3_addr + 1
$${\frac{\left({f_{14}\left(xg^{244}\right)} - {f_{16}\left(xg^{124}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [175] hash2-pre_round_1
$${\frac{{f_{14}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {2} + {f_{15}\left(xg^{108}\right)} \cdot {1} + {f_{16}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [176] hash2-pre_round_2
$${\frac{{f_{15}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {1} + {f_{15}\left(xg^{108}\right)} \cdot {2} + {f_{16}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [177] hash2-pre_round_3
$${\frac{{f_{16}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {1} + {f_{15}\left(xg^{108}\right)} \cdot {1} + {f_{16}\left(xg^{108}\right)} \cdot {2}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [178] hash2-hash_full_1_sq
$${\frac{\left({f_{26}\left(x\right)} - {\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [179] hash2-hash_full_2_sq
$${\frac{\left({f_{14}\left(xg^{4}\right)} - {\left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [180] hash2-hash_full_3_sq
$${\frac{\left({f_{15}\left(xg^{4}\right)} - {\left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [181] hash2-hash_full_next1
$${\frac{\left({f_{14}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [182] hash2-hash_full_next2
$${\frac{\left({f_{15}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [183] hash2-hash_full_next3
$${\frac{\left({f_{16}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {2}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$
## [184] hash2-hash_part_1_sq
$${\frac{\left({f_{26}\left(x\right)} - {\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [185] hash2-hash_part_next1-continuation
$${\frac{\left({f_{14}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [186] hash2-hash_part_next1-jump
$${\frac{\left({f_{14}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [187] hash2-hash_part_next2-continuation
$${\frac{\left({f_{15}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [188] hash2-hash_part_next2-jump
$${\frac{\left({f_{15}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [189] hash2-hash_part_next3-continuation
$${\frac{\left({f_{16}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$
## [190] hash2-hash_part_next3-jump
$${\frac{\left({f_{16}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$
## [191] hash2-hash_part_start1
$${\frac{{f_{14}\left(xg^{64}\right)} - {f_{14}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [192] hash2-hash_part_start2
$${\frac{{f_{15}\left(xg^{64}\right)} - {f_{15}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [193] hash2-hash_part_start3
$${\frac{{f_{16}\left(xg^{64}\right)} - {f_{16}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [194] hash2-hash_part_end1
$${\frac{{f_{14}\left(xg^{111}\right)} - {f_{14}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [195] hash2-hash_part_end2
$${\frac{{f_{15}\left(xg^{111}\right)} - {f_{15}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [196] hash2-hash_part_end3
$${\frac{{f_{16}\left(xg^{111}\right)} - {f_{16}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [197] vx1-vx_start
$${\frac{{f_{20}\left(xg^{3}\right)} - \left(\mathrm{vx\_start} + 0 \cdot {3} \cdot {\frac{T}{{128}}}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$
## [198] vx1-vx_in2_addr = vx_in1_addr + 1
$${\frac{{f_{20}\left(xg^{19}\right)} - {f_{20}\left(xg^{3}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [199] vx1-vx_out_addr = vx_in2_addr + 1
$${\frac{{f_{20}\left(xg^{35}\right)} - {f_{20}\left(xg^{19}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [200] vx1-vx_next_in1_addr = vx_out_addr + 1
$${\frac{\left({f_{20}\left(xg^{131}\right)} - {f_{20}\left(xg^{35}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [201] vx1-vx_f_mul copied
$${\frac{\left({f_{17}\left(xg^{7}\right)} - {f_{17}\left(xg^{3}\right)}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [202] vx1-vx_f_mul is bit
$${\frac{{{f_{17}\left(xg^{3}\right)}}^{{2}} - {f_{17}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [203] vx1-vx_v1_diff_chain_start is bit
$${\frac{{{f_{19}\left(xg^{3}\right)}}^{{2}} - {f_{19}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [204] vx1-vx_v1_diff_chain_diff is bit
$${\frac{\left({\left({f_{19}\left(xg^{19}\right)} - {2} \cdot {f_{19}\left(xg^{3}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{19}\right)} - {2} \cdot {f_{19}\left(xg^{3}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [205] vx1-vx_v2_diff_chain_start is bit
$${\frac{{{f_{19}\left(xg^{7}\right)}}^{{2}} - {f_{19}\left(xg^{7}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [206] vx1-vx_v2_diff_chain_diff is bit
$${\frac{\left({\left({f_{19}\left(xg^{23}\right)} - {2} \cdot {f_{19}\left(xg^{7}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{23}\right)} - {2} \cdot {f_{19}\left(xg^{7}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [207] vx1-vx_v3_diff_chain_start is bit
$${\frac{{{f_{19}\left(xg^{11}\right)}}^{{2}} - {f_{19}\left(xg^{11}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [208] vx1-vx_v3_diff_chain_diff is bit
$${\frac{\left({\left({f_{19}\left(xg^{27}\right)} - {2} \cdot {f_{19}\left(xg^{11}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{27}\right)} - {2} \cdot {f_{19}\left(xg^{11}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$
## [209] vx1-vx v1_begin
$${\frac{{f_{17}\left(xg^{3}\right)} \cdot {\mathrm{100000000000000000000}_{16}} + {f_{19}\left(xg^{115}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(x\right)} - {f_{20}\left(xg^{7}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [210] vx1-vx v2_begin
$${\frac{{f_{19}\left(xg^{119}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(xg\right)} - {f_{20}\left(xg^{23}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [211] vx1-vx v3_begin
$${\frac{{f_{19}\left(xg^{123}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(xg^{2}\right)} - {f_{20}\left(xg^{39}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [212] vx1-vx v1_stride
$${\frac{{f_{17}\left(xg^{4}\right)} - {f_{17}\left(x\right)} - {f_{19}\left(xg^{115}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [213] vx1-vx v2_stride
$${\frac{{f_{17}\left(xg^{5}\right)} - {f_{17}\left(xg\right)} - {f_{19}\left(xg^{119}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [214] vx1-vx v3_stride
$${\frac{{f_{17}\left(xg^{6}\right)} - {f_{17}\left(xg^{2}\right)} - {f_{19}\left(xg^{123}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$
## [215] vx1-vx product
$${\frac{{f_{18}\left(xg^{3}\right)} - {f_{18}\left(x\right)} \cdot {f_{18}\left(xg\right)}}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [216] vx1-vx result
$${\frac{{f_{18}\left(xg^{2}\right)} - \left({f_{17}\left(xg^{3}\right)} \cdot {f_{18}\left(xg^{3}\right)} + \left({1} - {f_{17}\left(xg^{3}\right)}\right) \cdot \left({f_{18}\left(x\right)} + {f_{18}\left(xg\right)}\right)\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [217] vx1-vx v1_addr is arithmetic
$${\frac{\left({f_{17}\left(xg^{8}\right)} - {f_{17}\left(xg^{4}\right)} - \left({f_{17}\left(xg^{4}\right)} - {f_{17}\left(x\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [218] vx1-vx v2_addr is arithmetic
$${\frac{\left({f_{17}\left(xg^{9}\right)} - {f_{17}\left(xg^{5}\right)} - \left({f_{17}\left(xg^{5}\right)} - {f_{17}\left(xg\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$
## [219] vx1-vx v3_addr is arithmetic
$${\frac{\left({f_{17}\left(xg^{10}\right)} - {f_{17}\left(xg^{6}\right)} - \left({f_{17}\left(xg^{6}\right)} - {f_{17}\left(xg^{2}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$